Phase diagrams defined

As most experiments are carried out at atmospheric pressure, a planar diagram, using temperature and composition as variables, is sufficient for many purposes. These sections at a fixed pressure are called isobaric phase diagrams. In these constant-pressure diagrams a single phase occurs over an area in the figure, and phase boundaries are drawn as hues. A point in such a binary phase diagram defines the temperature and composition of the system. 

By this calculation we obtain one tie line on the phase diagram, defined by the values of pressure, temperature, and composition of the two phases ... 

The Kroger-Vink diagram (Fig. 5.38) reproduces the internal chemistry within the homogeneity region of the phase (see Chapter 4). The connection between the exact position in the phase diagram defined by 6,(see Elq. (5.111)) and the equilibrium partial pressure is determined by an expression of the form a — b P l l. When... 

Flalf a century later Van Konynenburg and Scott (1970, 1980) [3] used the van der Waals equation to derive detailed phase diagrams for two-component systems with various parameters. Unlike van Laar they did not restrict their treatment to the geometric mean for a g, and for the special case of b = hgg = h g (equalsized molecules), they defined two reduced variables. 

When the iateraction energy density is positive, equation 5 defines a critical temperature of the UCST type (Fig. la) that is a function of component molecular weights. The LCST-type phase diagram, quite common for polymer blends, is not predicted by this simple theory unless B is... 

Ternary Alloys. Almost ah commercial ahoys are of ternary or higher complexity. Ahoy type is defined by the nature of the principal ahoying additions, and phase reactions in several classes of ahoys can be described by reference to ternary phase diagrams. Minor ahoying additions may have a powerflil influence on properties of the product because of the influence on the morphology and distribution of constituents, dispersoids, and precipitates. Phase diagrams, which represent equhibrium, may not be indicative of these effects. 

It would be incomplete for any discussion of soap crystal phase properties to ignore the colloidal aspects of soap and its impact. At room temperature, the soap—water phase diagram suggests that the soap crystals should be surrounded by an isotropic Hquid phase. The colloidal properties are defined by the size, geometry, and interconnectiviness of the soap crystals. Correlations between the coUoid stmcture of the soap bar and the performance of the product are somewhat quaUtative, as there is tittle hard data presented in the literature. However, it might be anticipated that smaller crystals would lead to a softer product. Furthermore, these smaller crystals might also be expected to dissolve more readily, leading to more lather. Translucent and transparent products rely on the formation of extremely small crystals to impart optical clarity. 

The other place where the constitution is not fully defined is where there is a horizontal line on the phase diagram. The lead-tin diagram has one line like this - it runs across the diagram at 183°C and connects (Sn) of 2.5 wt% lead, L of 38.1% lead and (Pb) of 81% lead. Just above 183°C an alloy of tin -i- 38.1% lead is single-phase liquid (Fig. 3.5). Just below 183°C it is two-phase, (Sn) -i- (Pb). At 183°C we have a three-phase mixture of L -I- (Sn) -I- (Pb) but we can t of course say from the phase diagram what the relative weights of the three phases are. 

What defines the constitution of an alloy If you can t remember, refer back to the definition on p. 311 and revise. The phase diagram gives all three pieces of information. The first you know already. This section explains how to get the other two. 

Fig. 16 presents a eomparison of the phase diagrams for eonfined (sohd lines) and bulk fluids (dashed lines). The average density in the pore Pp is defined as... 

Of course, LC is not often carried out with neat mobile-phase fluids. As we blend solvents we must pay attention to the phase behavior of the mixtures we produce. This adds complexity to the picture, but the same basic concepts still hold we need to define the region in the phase diagram where we have continuous behavior and only one fluid state. For a two-component mixture, the complete phase diagram requires three dimensions, as shown in Figure 7.2. This figure represents a Type I mixture, meaning the two components are miscible as liquids. There are numerous other mixture types (21), many with miscibility gaps between the components, but for our purposes the Type I mixture is Sufficient. 

The Phase Boundaries. Our interest in the phase diagram is solely to define the method by which the calculation of the partial pressures should be done. Because (1) there are only small... 

The phase diagram that we shall use to define the method of calculation is given in Figure 2. The regions are defined by ... 

FIGURE 8.6 The phase diagram for water (not to scale). The solid blue lines define the boundaries of the regions of pressure and temperature at which each phase is the most stable. Note that the freezing point decreases slightlv with increasing pressure. The triple point is the point at which three phase boundaries meet. The letters A and B are referred to in Example 8.3. 

A triple point is a point where three phase boundaries meet on a phase diagram. For water, the triple point for the solid, liquid, and vapor phases lies at 4.6 Torr and 0.01°C (see Fig. 8.6). At this triple point, all three phases (ice, liquid, and vapor) coexist in mutual dynamic equilibrium solid is in equilibrium with liquid, liquid with vapor, and vapor with solid. The location of a triple point of a substance is a fixed property of that substance and cannot be changed by changing the conditions. The triple point of water is used to define the size of the kelvin by definition, there are exactly 273.16 kelvins between absolute zero and the triple point of water. Because the normal freezing point of water is found to lie 0.01 K below the triple point, 0°C corresponds to 273.15 K. 

In each of the composition diagrams in Fig. 14.2, the numbers represent a series of reactions run at a defined composition and temperature. These are isometric sulfur slices through three-dimensional K/P/RE/S quaternary phase diagrams. As just one example of what we have studied. Table 14.1 identifies the compositions at each point and the resulting phase(s). We have rigorously studied how phase formation is dependent upon the compositions of reactions for the rare-earth elements Y, Eu, and La and we have also discovered key structural relationships between the rare-earth elements, indicating a significant dependence on rare-earth and alkali-metal size for sulfides and selenides. 

Figure 3.7) [241], Some consider the SCF state to be more extended and comprising the area of the phase diagram above Tc independent of p0 [242], Critical temperature and pressure are usually defined as the maximum temperature at which a gas can be converted to a liquid by an increase in pressure, and the maximum pressure at which a liquid can be converted to a gas by an increase in temperature, respectively. In a PT diagram the vaporisation curve ends at the critical point. At a temperature above the critical point, the vapour and liquid have the same density. The critical parameters for some common fluids in analytical studies are listed in Table 3.11, but others may be found elsewhere [243], in particular, rc = 31.3 °C and pc = 7.38MPa for the most common SCF (C02). Supercritical C02 (scC02) is widely used because of its convenient critical parameters, low cost, and safety aspects (low toxicity, nonexplosive). 

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